We propose in the renewal of this MERIT award application to continue developing advanced statistical and computational methods for analysis of correlated and high-dimensional data, which arise frequently in health science research, especially in cancer research. Correlated data are often observed in observational studies and clinical trials, such as longitudinal studies and familial studies. High-dimensional data have emerged rapidly in recent years due to the advance of high-throughput 'omics technologies, e.g, in Genome- Wide Association Studies (GWAS), and genome-wide epigenetic (DNA methylation) studies. Massive next generation sequencing data are soon available. There is an urgent need to develop advanced stati stical and computational methods for analyzing such high throughput 'omics data in observational studies and clinical trials. We propose to develop statistical and computational methods for analysis of (1) genome-wide association studies;(2) sequencing data for studying rare variant effects;(3) genome-wide DNA methylation studies;(4) gene-gene and gene-environment interactions. We will develop methods for both case-control studies and cohort studies, such as longitudinal studies and survival studies. We will study the theoretical properties of the proposed methods and evaluate the finite s ample performance using simulation studies. We will develop efficient numerical algorithms and user-friendly statistical software, and disseminate these tools to health sciences researchers. In collaboration with biomedical investigators, we will apply the proposed models methods to data from several genome-wide epidemiological studies in cancer and other chronic diseases.